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KiRa [710]
3 years ago
7

Write 2^40 as an exponent with a base of: a 2^2; b 2^5; c 2^8; 2^10

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
6 0

Answer:

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify.

Exact Form:  a = 6, 2 3

Decimal Form: a = 6 , 0. ¯ 6

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Eugene walked all the way to school at 3 mph then realized she forgot her math book (how could she?!), so she ran back at 7 mph.
Fynjy0 [20]

\text{Answer: }1\frac{23}{40}\ miles\text{ far she live from school.}

Explanation:

Since we have given that

Speed at which Eugene walked all the way to school = 3 mph

After realizing that she forgot her math book, she ran back

Speed at which Eugene walked back to her house = 7 mph

Let the distance between her house and her school be x

According to question,

\frac{x}{3}+\frac{x}{7}=\frac{45}{60}\\\\\frac{7x+3x}{21}=\frac{3}{4}\\\\\frac{10x}{21}=\frac{3}{4}\\\\x=\frac{3\times 63}{4\times 10}=\frac{63}{40}=1\frac{23}{40}\ miles.

Hence,

1\frac{23}{40}\ miles\text{ far she live from school.}

8 0
2 years ago
Frank purchased a new ice box having 2kg capacity. He wants it to be full with ice cubes. He measured the ice cubes to be 3.5 cm
salantis [7]

Answer:

Frank can put 5 cubes in the box.

Step-by-step explanation:

Formula:

Mass = Volume × density.

1 cubic centimetre = 0.001 liter= 1 millilitre

Given that,

Frank purchase a new ice box having 2 kg capacity.

So,the mass of the cubes is 2 kg.

Each ice cubes measured 3.5 cm by 3.5 cm by 3.5 cm.

The volume of a cube is = Side ^3

The volume of a each ice cubes is =3.5^3 cm³

                                                        = 42.875 ml

The ice cubes have a density of 0.914 g/ml

The mass of each cubes are

=volume of each ice cubes × density

=42.875 ml ×0.914 g/ml

=39.18775 gram.

Let x number of ice cubes he can put in the box.

The mass of x cubes is = 39.18775x grams.

2 kg= 2,000 gram [ since 1 kg= 1000 gram]

According to the problem,

39.18775x=2,000

\Rightarrow x=\frac{2000}{39.18775}

\Rightarrow x\approx 51

Frank can put 5 cubes in the box.

5 0
3 years ago
What is Rational Number​
abruzzese [7]
Rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
8 0
1 year ago
Read 2 more answers
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Paladinen [302]
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8 0
2 years ago
Solve for x: sinx-cosx=√2
kvv77 [185]
<span>sinx - cosx =sqrt(2)
Taking square on both sides:
</span>(sinx - cosx)^2 =sqrt(2)^2<span>
sin^2(x) -2cos(x)sin(x) + cos^2(x) = 2
Rearranging the equation:
sin^2(x)+cos^2(x) -2cos(x)sin(x)=2
As,
</span><span>sin^2(x)+cos^2(x) = 1
</span><span>So,
1-2sinxcosx=2
 1-1-2sinxcosx=2-1
 -</span><span>2sinxcosx = 1
</span><span>Using Trignometric identities:
-2(0.5(sin(x+x)+sin(x-x))=1 
-sin2x+sin0=1
As,
sin 0 = 0
So,
sin2x+0 = -1
</span><span>sin2x = -1</span><span>
2x=-90 degrees + t360
Dividing by 2 on both sides:
x=-45 degrees + t180
or 2x=270 degrees +t360
x= 135 degrees + t180 where t is integer</span>
6 0
3 years ago
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